Orbe: Scalable Causal Consistency Using Dependency Matrices

Orbe: Scalable Causal Consistency
Using Dependency Matrices and Physical Clocks
Jiaqing Du? , Sameh Elnikety† , Amitabha Roy? , Willy Zwaenepoel?
? EPFL
† Microsoft Research
Abstract
We propose two protocols that provide scalable causal
consistency for both partitioned and replicated data
stores using dependency matrices (DM) and physical
clocks. The DM protocol supports basic read and update
operations and uses two-dimensional dependency matrices to track dependencies in a client session. It utilizes
the transitivity of causality and sparse matrix encoding
to keep dependency metadata small and bounded. The
DM-Clock protocol extends the DM protocol to support
read-only transactions using loosely synchronized physical clocks.
We implement the two protocols in Orbe, a distributed
key-value store, and evaluate them experimentally. Orbe
scales out well, incurs relatively small overhead over an
eventually consistent key-value store, and outperforms
an existing system that uses explicit dependency tracking to provide scalable causal consistency.
1
Introduction
Distributed data stores are a critical infrastructure component of many online services. Choosing a consistency
model for such data stores is difficult. The CAP theorem [7, 10] shows that among Consistency, Availability, and (network) Partition-tolerance, a replicated system can only have two properties out of the three.
A strong consistency model, such as linearizability
[11] and sequential consistency [15], does not allow high
availability under network partitions. In contrast, eventual consistency [24], a weak model, provides high avail-
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ability and partition-tolerance, as well as low update latency. It guarantees that replicas eventually converge to
the same state provided no updates take place for a long
time. However, it does not guarantee any order on applying replicated updates. Causal consistency [2] is weaker
than sequential consistency but stronger than eventual
consistency. It guarantees that replicated updates are applied at each replica in an order that preserves causality
[2, 14] while providing availability under network partitions. Furthermore, client operations have low latency
because they are executed at a local replica and do not
require coordination with other replicas.
The problem addressed in this paper is providing a
scalable and efficient implementation of causal consistency for both partitioned and replicated data stores.
Most existing causally consistent systems [13, 19, 22]
adopt variants of version vectors [2, 21], which are designed for purely replicated data stores. Version vectors
do not scale when partitioning is added to support a
data set that is too large to fit on a single server. They
still view all partitions as one logical replica and require
a single serialization point across partitions for replication, which limits the replication throughput [17]. A
scalable solution should allow replicas of different partitions to exchange updates in parallel without serializing
them at a centralized component.
COPS [17] identifies this problem and provides a solution that explicitly tracks causal dependencies at the
client side. A client stores every accessed item as dependency metadata and associates this metadata with each
update operation issued to the data store. When an update is propagated from one replica to another for replication, it carries the dependency metadata. The update
is applied at the remote replica only when all its dependencies are satisfied at that replica. COPS provides good
scalability. However, tracking every accessed item explicitly can lead to large dependency metadata, which
increases storage and communication overhead and affects throughput. Although COPS employs a number of
techniques to reduce the size of dependency metadata, it
does not fundamentally solve the problem. When supporting causally consistent read-only transactions, the
dependency metadata overhead is still high under many
workloads.
In this paper, we present two protocols and one optimization that provide a scalable and efficient implementation of causal consistency for both partitioned and
replicated data stores.
The first protocol uses two-dimensional dependency
matrices (DMs) to compactly track dependencies at the
client side. We call it the DM protocol. This protocol
supports basic read and update operations. It associates
with each update the dependency matrix of its client session. Each element in a dependency matrix is a scalar
value that represents all dependencies from the corresponding data store server. The size of dependency matrices is bounded by the total number of servers in the
system. Furthermore, the DM protocol resets the dependency matrix of a client session after each update operation, because prior dependencies need not to be tracked
due to the transitivity of causality. With sparse matrix
encoding, the DM protocol keeps the dependency metadata of each update small.
The second protocol extends the DM protocol to support causally consistent read-only transactions by using loosely synchronized physical clocks. We call it the
DM-Clock protocol. In addition to the dependency metadata required by the DM protocol, this protocol assigns
to each state an update timestamp obtained from a local physical clock and guarantees that the update timestamp order of causally related states is consistent their
causal order. With this property, the DM-Clock protocol
provides causally consistent snapshots of the data store
to read-only transactions by assigning them a snapshot
timestamp, which is also obtained from a local physical
clock.
We also propose dependency cleaning, an optimization that further reduces the size of dependency metadata in the DM and DM-Clock protocols. It is based on
the observation that once a state and its dependencies are
fully replicated, any subsequent read on the state does
not introduce new dependencies to the client session.
More messages need to be exchanged, however, for a
server to be able to decide that a state is fully replicated,
which leads to a tradeoff which we study. Dependency
cleaning is a general technique and can be applied to
other causally consistent systems.
We implement the two protocols and dependency
cleaning in Orbe, a distributed key-value store, and evaluate them experimentally. Our evaluation shows that
Orbe scales out as the number of data partitions increases. Compared with an eventually consistent system, it incurs relatively little performance overhead for a
large spectrum of workloads. It outperforms COPS under many workloads when supporting read-only transactions.
Application Tier
Client
Client
Client
Data Center
Data Server
Data Server
Data Center
Data Center
Figure 1: System architecture. The data set is replicated by
multiple data centers. Clients are collocated with the data store
in the data center and are used by the application tier to access
the data store.
In this paper, we make the following contributions:
• The DM protocol that provides scalable causal consistency and uses dependency matrices to keep the
size of dependency metadata under control.
• The DM-Clock protocol that provides read-only
transactions with causal snapshots using loosely
synchronized physical clocks by extending the DM
protocol.
• The dependency cleaning optimization that reduces
the size of dependency metadata.
• An implementation of the above protocols and optimization in Orbe as well as an extensive performance evaluation.
2
Model and Definition
In this section we describe our system model and define
causality and causal consistency.
2.1
Architecture
We assume a distributed key-value store that manages
a large set of data items. The key-value store provides
two basic operations to the clients:
• PUT(key, val): A PUT operation assigns value val
to an item identified by key. If item key does not exist, the system creates a new item with initial value
val. If key exists, a new version storing val is created.
• val ← GET(key): The GET operation returns the
value of the item identified by key.
An additional operation that provides read-only transactions is introduced later in Section 4.
The data store is partitioned into N partitions, and
each partition is replicated by M replicas. A data item is
assigned to a partition based on the hash value of its key.
In a typical configuration, as shown in Figure 1, the data
store is replicated at M different data centers for high
availability and low operation latency. The data store is
fully replicated. All N partitions are present at each data
center.
The application tier relies on the clients to access the
underlying data store. A client is collocated with the data
store servers in a particular data center and only accesses
those servers in the same data center. A client does not
issue the next operation until it receives the reply to the
current one. Each operation happens in the context of a
client session. A client session maintains a small amount
of metadata that tracks the dependencies of the session.
2.2
Causal Consistency
Causality is a happens-before relationship between
two events [2, 14]. We denote causal order by . For
two operations a and b, if a b, we say b depends on a
or a is a dependency of b. a b if and only if one of the
following three rules holds:
• Thread-of-execution. a and b are in a single thread
of execution. a happens before b.
• Reads-from. a is a write operation and b is a read
operation. b reads the state created by a.
• Transitivity. There is some other operation c that
a c and c b.
We define the nearest dependencies of a state as all
the states that it directly depends on, without relying on
the transitivity of causality.
To provide causal consistency when replicating updates, a replica does not apply an update propagated
from another replica until all its causal dependency
states are installed locally.
3
DM Protocol
In this section, we present the DM protocol that provides
scalable causal consistency using dependency matrices.
This protocol is scalable because replicas of different
partitions exchange updates for replication in parallel,
without requiring a global serialization point.
Dependency matrices are, for systems that support
both replication and partitioning, the natural extension
of version vectors, for systems that support only replication. A row of a dependency matrix is a version vector
that stores the dependencies from replicas of a partition.
A client stores the nearest dependencies of its session
in a dependency matrix and associates it with each update request to the data store. After a partition at the
client’s local data center executes the update, it propagates the update with its dependency matrix to the replicas of that partition at remote data centers. Using the dependency matrix of the received update, a remote replica
Symbols
N
M
c
DMc
PDTc
pm
n
VVnm
PVVnm
Clocknm
d
k
v
ut
put
dm
rid
t
st
rs
Definitions
number of partitions
number of replicas per partition
a client
dependency matrix of c, N × M elements
physical dependency timestamp of c
a server that runs mth replica of nth partition
(logical) version vector of pm
n , M elements
physical version vector of pm
n , M elements
current physical clock time of pm
n
an item, tuple hk, v, ut, put 1 , dm, ridi
item key
item value
(logical) update timestamp
physical update timestamp
dependency matrix, N × M elements
source replica id
a read-only transaction, tuple hst, rsi
(physical) snapshot timestamp
readset, a set of read items
Table 1: Definition of symbols.
waits to apply the update until all partitions at its data
center store the dependency states of the update.
3.1
Definitions
The DM protocol introduces dependency tracking
data structures at both the client and server side. It also
associates dependency metadata for each item. Table 1
provides a summary of the symbols used in the protocol.
We explain their meanings in details below.
Client States. Without losing generality, we assume
a client has one session to the data store. A client c
maintains for its session a dependency matrix, DMc ,
which consists of N × M non-negative integer elements.
DMc tracks the nearest dependencies of a client session.
DMc [n][m] indicates that the client session potentially
depends on the first DMc [n][m] updates at partition pm
n,
the mth replica of the nth partition.
Server States. Each partition maintains a version vector (VV) [2, 21]. The version vector of partition pm
n
is VVnm , which consists of M non-negative integer elements. VVnm [m] counts the number of updates pm
n has
executed locally. VVnm [i] (i 6= m) indicates that pm
n has
applied the first VVnm [i] updates propagated from pin , a
replica of the same partition.
A partition updates an item by either executing an update request from its clients or by applying a propagated
update from one of its replicas at other data centers. We
call the partition that updates an item to the current value
by executing a client request the source partition of the
item.
Item Metadata. We represent an item d as a tuple
1 put
is only used in the DM-Clock protocol.
hk, v, ut, dm, ridi. k is a unique key that identifies the
item. v is the value of the item. ut is the update timestamp, the logical creation time of the item at its source
partition. dm is the dependency matrix, which consists
of N × M non-negative integer elements. dm[n][m] indicates that d potentially depends on the first dm[n][m] updates at partition pm
n , a prefix of its update history. rid is
the source replica id, the replica id of the item’s source
partition.
We use sparse matrix encoding to encode dependency
matrices. Zero elements in a dependency matrix do not
use any bits after encoding. Only non-zero elements contribute to the actual size.
3.2
Protocol
We now describe how the DM protocol executes GET
and PUT operations and replicates PUTs.
GET. Client c sends a request hG ET ki to a
partition at the local data center, where k is the
key of the item to read. Upon receiving the request, partition pm
n obtains the read item, d, and
sends a reply hG ET R EPLY vd , utd , ridd i back to
the client. Upon receiving the reply, the client
updates its dependency matrix: DMc [n][ridd ] ←
max(DMc [n][ridd ], utd ). It then hands the read value, vd ,
to the caller of GET.
PUT. Client c sends a request hP UT k, v, DMc i to a
partition at the local data center, where k is the item key
and v is the update value. Upon receiving the request,
m
pm
n performs the following steps: 1) Increment VVn [m];
2) Create a new version d for the item identified by
k; 3) Assign item key: kd ← k; 4) Assign item value:
vd ← v; 5) Assign update timestamp: utd ← VVnm [m];
6) Assign dependency matrix: dmd ← DMc ; 7) Assign
source replica id: ridd ← m. These steps form one atomic
operation, and none of them is blocking. pm
n stores d on
stable storage and overwrites the existing version if there
is one. It then sends a reply hP UT R EPLY utdd , ridd i back
to the client. Upon receiving the reply, the client updates
its dependency matrix: DMc ← 0 (reset all elements to
zero) and DMc [n][ridd ] ← utd .
Update Replication. A partition propagates its local
updates to its replicas at remote data centers in their
update timestamp order. To replicate a newly updated
item, d, partition psn sends an update replication request
hR EPLICATE kd , vd , utd , dmd , ridd i to all other replicas.
A partition also applies updates propagated from other
replicas in their update timestamp order. Upon receiving
the request, partition pm
n guarantees causal consistency
by performing the following steps:
1) pm
n checks if it has installed the dependency states
m
of d specified by dmd [n]. pm
n waits until VVn >
m
dmd [n], i.e., VVn [i] > dmd [n][i], for 0 6 i 6 M − 1.
Client
DM = [[0,0] [0,0]]
DM = [[1,0] [0,0]]
DM = [[0,0] [1,0]]
PUT(X)
Partition 0
X
Partition 1
Y
Replica 0
Replica 1
Partition 0
Partition 1
PUT(Y)
VV = [0,0]
VV = [0,0]
Y
dmY = [[1,0] [0,0]]
X
dmX = [[0,0] [0,0]]
VV = [1,0]
VV = [1,0]
Figure 2: An example of the DM protocol with two partitions
replicated at two data centers. A client updates item X and then
item Y at two partitions. X and Y are propagated concurrently
but their installation at the remote data center is constrained by
causality.
2) pm
n checks if causality is satisfied at the other local
m
partitions. pm
n waits until, VV j > dmd [ j], for 0 6
j 6 N − 1 and j 6= n. It needs to send a message to
pmj for dependency checking if dmd [ j] contains at
least one non-zero element.
3) If there is currently no value stored for item kd at
m
pm
n , it simply stores d. If pn has an existing version
d 0 such that kd 0 = kd , it orders the two versions deterministically by concatenating the update timestamp (high order bits) and source replica id (low
0
order bits). If d is ordered after d 0 , pm
n overwrites d
with d. Otherwise, d is discarded.
m
4) pm
n updates its version vector: VVn [s] ← utd . As updates are propagated in order, we have the invariant
before VVnm [s] is updated: VVnm [s] + 1 = utd .
Example. We give an example to explain the necessity for dependency matrices. Consider a system with
two partitions replicated at two data centers (N = 2 and
M = 2) in Figure 2. The client first updates item X at the
local data center. The update is handled by partition p00 .
Upon receiving a response the client updates item Y at
partition p01 . Causality through the client session dictates
that X
Y . At the other data center, p11 applies Y only
after p10 applies X. The figure shows the dependency matrices propagated with the updates. p11 waits until the version vector of p10 is no less than [1, 0], which guarantees
that X has been replicated.
Correctness. The DM protocol uses dependency matrices to track the nearest dependencies of a client session or an item. It resets the dependency matrix of a
client session after each PUT to keep its size after encoding small. This does not affect correctness. By only
remembering the update timestamp of the PUT, the protocol utilizes the transitivity of causality to track dependencies correctly.
An element in a dependency matrix, a scalar value,
is the maximum update timestamp of all the nearest dependency items from the corresponding partition. Since
a partition always propagates local updates to and applies remote updates from other replicas in their update
timestamp order, once it applies an update from another
replica, it must have applied all the other updates with a
smaller update timestamp from the same replica. Therefore, if a partition satisfies the dependency requirement
specified by the dependency matrix of an update, it must
have installed all the dependencies of the update.
3.3
Cost over Eventual Consistency
Compared with typical implementations of eventual
consistency, the DM protocol introduces some overhead
to capture causality. This is a reasonable price to pay for
the stronger semantics.
Storage Overhead. The protocol keeps a dependency
matrix and other metadata for each item. The per-item
dependency metadata is the major storage overhead of
causal consistency. We keep it small by only tracking
the nearest dependencies and compressing it by sparse
matrix encoding. In addition, the protocol requires that a
client session maintains a dependency matrix and a partition maintains a version vector. These global states are
small and negligible.
Communication Overhead. Checking dependencies
of an update during replication requires a partition to
send a maximum of N − 1 messages to other local partitions. If a row in the dependency matrix contains all
zeros, then the corresponding partition does not need to
be checked since the update does not directly depend
on any states managed by all replicas of that partition.
In addition, the dependency metadata carried by update
replication messages also contributes to inter-datacenter
network traffic.
3.4
Conflict Detection and Resolution
The above protocol orders updates of the same item
deterministically by using the update timestamp and
source replica id. If there are no updates for a long
enough time, replicas of the same partition eventually
converge to the same state while respecting causality.
However, the dependency metadata does not indicate
whether two updates from different replicas are conflicting or not.
To support conflict detection, we extend the DM protocol by introducing one more member to the existing
dependency metadata: the item dependency timestamp.
We denote the item dependency timestamp of an item
d by idtd . When d’s source partition psn creates d, it assigns to idtd the update timestamp of the existing version
of item kd if it exists or -1 otherwise. When partition pm
n
applies d after dependency checking, it handles the existing version d 0 as below. If d is created after d 0 is repli-
cated at psn , idtd = utd 0 , then d and d 0 do not conflict.
0
0
pm
n overwrites d with d. If d and d are created concurrently by different replicas, idtd 6= utd 0 , they conflict. In
that case, either the application can be notified to resolve
the conflict using application semantics, or pm
n orders the
two conflicting updates deterministically as outlined in
Section 3.2.
4
DM-Clock Protocol
In this section, we describe the DM-Clock protocol,
which extends the DM protocol to support causally consistent read-only transactions. Many applications can
benefit from a programming interface that provides a
causally consistent view on multiple items, as an example later in this section shows.
Compared with the DM protocol, the DM-Clock protocol keeps multiple versions of each item. It also requires accesses to physical clocks. It assigns each item
version a physical update timestamp, which imposes on
causally related item versions a total order consistent
with the (partial) causal order. A read-only transaction
obtains its snapshot timestamp by reading the physical
clock at the first partition it accesses, its originating partition. The DM-Clock protocol then provides a causally
consistent snapshot of the data store, including the latest item versions with a physical update timestamp no
greater than the transaction’s snapshot timestamp.
4.1
Read-only Transaction
With the DM-Clock protocol, the key-value store also
provides a transactional read operation:
• hvalsi ← GET-TX(hkeysi): This operation returns
the values of a set of items identified by keys. The
returned values are causally consistent.
A read-only transaction provides a causally consistent
snapshot of the data store. Assume xr and yr are two versions of items X and Y , respectively. If a read-only transaction reads xr and yr , and xr
yr , then there does not
exist another version of X, xo , such that xr
xo yr .
We give a concrete example to illustrate the application of read-only transactions. Assume Alice wants to
share some photos with friends through an online social
network such as Facebook. She first changes the permission of an album from “public” to “friends-only” and
then uploads some photos to that album. When these two
updates are propagated to and applied at remote replicas, causality ensures that their occurrence order is preserved: the permission update operation happens before
the photo upload operation. However, it is possible that
Bob, not a friend of Alice, first reads the permission of
the album as “public” and then sees the photos that were
uploaded after the album was changed to “friends-only”.
Enclosing the album permission check and the viewing
of the photos in a causally consistent read-only transaction prevents this undesirable outcome. In a causally
consistent snapshot, the photos cannot be viewed if the
permission change that causally precedes their uploads
is not observed.
4.2
Definitions
Physical Clocks. The DM-Clock protocol uses
loosely synchronized physical clocks. We assume each
server is equipped with a hardware clock that increases
monotonically. A clock synchronization protocol, such
as the Network Time Protocol (NTP) [1], keeps the clock
skew under control. The clock synchronization precision
does not affect the correctness of our protocol. We use
Clocknm to denote the current physical clock time at partition pm
n.
Dependency Metadata. Compared with the DM protocol, the DM-Clock protocol introduces additional dependency metadata. Each version of an item d has a
physical update timestamp, putd , which is the physical
clock time at the source partition of d when it is created.
Different versions of an item are sorted in the item’s
version chain using their physical update timestamps. A
client c maintains a physical dependency time, PDTc , for
its session. This variable stores the greatest physical update timestamp of all the states a client session depends
on. Each partition pm
n maintains a physical version vector, PVVnm , a vector of M physical timestamps. PVVnm [i]
(0 6 i 6 M − 1, i 6= m) indicates the physical time of pin
seen by pm
n . This value comes either from replicated updates or from heartbeat messages.
4.3
Protocol
We now describe how the DM-Clock protocol extends
the DM protocol to support read-only transactions.
GET. When a partition returns the read version d
back to the client, it also includes its physical update timestamp putd . Upon receiving the reply, the
client updates its physical dependency time: PDTc ←
max(PDTc , putd ).
PUT. An update request from client c to partition pm
n
also includes PDTc . When pm
n receives the request, it first
checks whether PDTc < Clocknm . If not, it delays the update request until the condition holds. When pm
n creates
a new version d for the item identified by kd , it also assigns d the physical update time: putd ← Clocknm . It then
inserts d to the version chain of item kd using utd . The reply message back to the client also includes putd . Upon
receiving the reply message, the client updates its physical dependency time: PDTc ← max(PDTc , putd ).
With the above read and update rules, our protocol provides the following property on causally related
states: For any two item versions x and y, if x y, then
putx < puty .
Update Replication. An update replication request of
d also includes putd . When partition pm
n receives d from
psn and after d’s dependencies are satisfied, it inserts d
into the version chain of item kd using putd . pm
n then
updates its physical version vector: PVVnm [s] ← putd .
Heartbeat Broadcasting. A partition periodically
broadcasts its current physical clock time to its replicas
at remote data centers. It sends out heartbeat messages
and updates in the physical timestamp order.
When pm
n receives a heartbeat message with physical time pt from psn , it updates its physical version vector: PVVnm [s] ← pt. We use ∆ to denote the heartbeat
broadcasting interval. (Our implementation of Orbe sets
∆ to 10ms.) A partition skips sending a heartbeat message to a replica if there was an outgoing update replication message to that replica within the previous ∆ time.
Hence, heartbeat messages are not needed when replicas
exchange updates frequently enough.
GET-TX. A read-only transaction t maintains a physical snapshot timestamp stt and a readset rst . Client c
sends a request hG ET T X kseti to a partition by some
load balancing algorithm, where kset is the set of items
to read.
When t is initialized at pm
o , the originating partition,
it reads the local hardware clock to obtain its snapshot timestamp: stt ← Clockom − ∆. We provide a slightly
older snapshot to a transaction, by subtracting some
amount of time from the latest physical clock time, to
reduce the probability of a transaction being delayed and
the duration of the delay. pm
o reads the items specified by
kset one by one. If pm
does
not store an item required
o
by t, it reads the item from another local partition that
stores the item.
Before t reads an item at partition pm
n , it first
waits until two conditions hold: 1) Clocknm > stt ; 2)
min({PVVnm [i] | 0 ≤ i ≤ M − 1, i 6= m}) > stt . t then
chooses the latest version d such that putd 6 stt from
the version chain of the read item and adds d to its readset rst . After t finishes reading all the requested items, it
sends a reply hG ET T X R EPLY rst i back to the client. The
client handles each retrieved item version in rst one by
one in the same way as for a GET operation.
By delaying a read-only transaction under the above
conditions, our protocol achieves the following property:
The snapshot of a transaction includes all item versions
with a physical update timestamp no greater than its
snapshot timestamp, if no failure happens.
If failure happens, a read-only transaction may be
blocked. We provide solutions to this in Section 5, where
we discuss failure handling.
Correctness. To see why our protocol provides
causally consistent read-only transactions, consider
xr
yr in the definition in Section 4.1 again. With the
first property, if a transaction t reads xr and yr , then
putxr < putyr ≤ stt . With the second property, t only
reads the latest version of an item with a physical update
timestamp no greater than stt . Hence there does not exist
xo such that putxr < putxo ≤ stt . Therefore, it is impossible that there exists xo such that xr
xo . Our protocol
provides causally consistent read-only transactions.
Conflict Detection and Resolution. The above DMClock protocol cannot tell whether two updates conflict or not. We employ the same technique used by the
DM protocol in Section 3.4 to detect conflicts. We do
not need the conflict resolution part here since the DMClock protocol uses physical update timestamps to totally order different versions of the same item.
4.4
Garbage Collection
The DM-Clock protocol stores multiple versions of
each item. We briefly describe how to garbage-collect
old item versions to keep the storage footprint small.
Partitions within the same data center periodically exchange snapshot timestamps of the oldest active transactions. If a partition does not have any active read-only
transactions, it sends out the latest physical clock time.
At each round of garbage collection, a partition chooses
the minimum one among the received timestamps as the
safe garbage collection timestamp. With this timestamp,
a partition scans the version chain of each item it stores.
It only keeps the latest item version created before the
safe garbage collection timestamp (if there is one) and
the versions created after the timestamp. It removes all
the other versions that are not needed by active and future read-only transactions.
5
Failure Handling
We briefly describe how the DM and DM-Clock protocols handle failures.
5.1
DM Protocol
Client Failures. When a client fails, it stops issuing
new requests to the data store. The failure of a client
does not affect other clients and the data store. Recovery
is not needed since a client only stores soft states for
dependency tracking.
Partition Server Failures. A partition maintains a
redo log on stable storage, which stores all installed update operations in the update timestamp order. A failed
partition recovers by replaying the log. Checkpointing
can be used to accelerate the recovery process. The partition then synchronizes its states with other replicas at
remote data centers by exchanging locally installed updates.
The current design of the DM protocol does not tolerate partition failures within a data center. However, it
can be extended to tolerate failures by replicating each
data partition within the same data center using standard
techniques, such as primary copy [4, 20], Paxos [16] and
chain replication [23].
Data Center Failures. The DM protocol tolerates
the failure of an entire data center, for example due to
power outage, and network partitions among data centers. If a data center fails and recovers later, it rebuilds
the data store states by recovering each partition in parallel. If the network partitions and heals later, it updates
the data store states by synchronizing the operation logs
within each replication group in parallel. If a data center fails permanently and cannot recover, any updates
originated in the failed data center, which are not propagated out, will be lost. This is inevitable due to the
nature of causally consistent replication, which allows
low-latency local updates without requiring coordination across data centers.
5.2
DM-Clock Protocol
The DM-Clock protocol uses the same failure handling techniques of the DM protocol, except that it treats
read-only transactions specially.
With the DM-Clock protocol, before reading an item
at a partition, a read-only transaction requires that the
partition has executed all local updates and applied all
remote updates with update timestamps no greater than
the snapshot timestamp of the transaction. However, if
a remote replica fails or the network among data centers partitions, a transaction might be delayed for a long
time because it does not know whether there are any updates from a remote replica that should be included in its
snapshot but have not been propagated.
Two approaches can solve this problem. If a transaction is delayed longer than a certain threshold, its originating partition re-executes it using a smaller snapshot
timestamp to avoid blocking on the (presumably) failed
or disconnected remote partition. With this approach, the
transaction provides relatively stale item versions until
the remote partition reconnects. A transaction delayed
for enough long time can also switch to a two-round protocol similar to the one used in Eiger [18]. In this case,
the transaction returns relatively fresh data but may need
two rounds of messages to finish.
6
Dependency Cleaning
In this section, we present dependency cleaning, a technique that further reduces the size of dependency metadata in the DM and DM-Clock protocols. This idea is
general and can be applied to other causally consistency
systems.
6.1
Intuition
Although our DM and DM-Clock protocols effectively reduce the size of dependency metadata by using dependency matrices and a few other techniques, for
big data sets managed by a large number of servers, it
is still possible that the dependency matrix of an update has many non-zero elements. For instance, a client
may scan a large number of items located at many different partitions and update a single item in some statistics
workloads. In this case, the dependency metadata can
be many times bigger than the actual application payload, which incurs more inter-datacenter traffic for update replication. In addition, checking dependencies of
such an update during replication requires a large number of messages.
The hidden assumption behind tracking dependencies
at the client side is that a client does not know whether
a state it accesses has been fully replicated by all replicas. To guarantee causal consistency, the client has to remember all the nearest dependency states it accesses and
associates them to subsequent update operations. Hence
when an update is propagated to a remote replica, the
remote replica uses its dependency metadata to check
whether all its dependency states are present there. This
approach is pessimistic because it assumes the dependency states are not replicated by all replicas. Most existing solutions for causal consistency are built on this
assumption. This is a valid assumption if the network
connecting the replicas fails or disconnects often, which
the early works are based upon [21, 22]. However, it is
not realistic for modern data center applications. Data
centers of the same organization are often connected by
high speed, low latency, and reliable fiber links. Most
of the time, network partitions among data centers only
happen because of accidents, and they are rare. Therefore, we argue that one should not be pessimistic about
dependency tracking for this type of applications. If a
state and its dependencies are known to be fully replicated by all replicas, a client does not need to include it
in the dependency metadata when reading it. With this
observation, we can substantially reduce the size of the
dependency metadata.
6.2
Protocol Extension
We describe how to extend the DM and DM-Clock
protocols to support dependency cleaning. To track updates that are replicated by all replicas, we introduce a
full replication version vector (RVV) at each partition.
m
m
At partition pm
n , RVVn indicates that the first RVVn [i]
i
updates of pn (0 6 i 6 M − 1) have been fully replicated.
Update Replication. We add the following extensions to the update replication process. After pm
n propagates an item version d to all other replicas, it requires them to send back a replication acknowledgment
message after they apply d. Similar to propagating local updates in their update timestamp order, a partition
also sends replication acknowledgments in the same order. Once pm
n receives replication acknowledgments of d
from all other replicas, it increments RVVnm [m]. pm
n then
sends a full-replication completion message of d to other
replicas. Similarly, the full-replication completion messages are also sent in the update timestamp order. Upon
partition pin receives the full-replication completion of d,
it increments RVVni [m] (0 6 i 6 M − 1 and i 6= m). Since
m
partition pm
n increments an element of VVn when applying a replicated update but increments the corresponding
element in RVVnm only after that update is fully replicated, RVVnm 6 VVnm always holds.
GET and GET-TX. We now describe how RVV is
used to perform dependency cleaning when the data
store handles read operations. Assume a client sends a
read request to partition pm
n and an item version d is selected. If RVVnm [ridd ] > utd , pm
n knows that d and all its
dependency states have been fully replicated and there
is no need to include d in the dependencies of the client
session. pm
n sends a reply message back to the client
without including d’s update timestamp. Upon receiving the reply, the client keeps its dependency matrix unchanged. This technique can also be applied to read-only
transactions similarly. Therefore, by marking an item
version as fully replicated, this technique “cleans” the
dependency it introduces to the client that reads it.
Normally, the duration that RVVnm [ridd ] < utd holds
is short. Under moderate system loads, this duration
is roughly 1.5 WAN round-trip latency plus two times
the write latency of stable storage , which is normally
a few hundreds milliseconds. As a consequence, for a
broad spectrum of applications, most read operations do
not generate dependencies, which keeps the dependency
metadata small.
6.3
Message Overhead
Dependency cleaning has a tradeoff. It reduces the
size of dependency metadata and the cost of dependency checking at the expense of more network messages for sending replication acknowledgments and fullreplication completions.
Assume an update depends on states from k partitions
except its source partition. For a system with M replicas, without dependency cleaning, it takes M − 1 WAN
messages to propagate the update to all other replicas at
remote data centers. The dependency matrix in each of
the M − 1 WAN messages has at least k non-zero rows.
(M − 1)k LAN messages are required for checking dependencies of the propagated update at remote replicas.
With dependency cleaning, it requires 3(M − 1) WAN
messages to replicate an update. For many workloads,
the dependency matrix of an update contains mostly zero
elements. Almost no LAN messages are needed for dependency checking.
7
Evaluation
We evaluate the DM protocol, DM-Clock protocol, and
dependency cleaning in Orbe, a multiversion key-value
store that supports both partitioning and replication. In
particular, we answer the following questions:
• Does Orbe scale as the number of partitions increases?
• What is the overhead of providing causal consistency compared with eventual consistency?
• How does Orbe compare with COPS?
• Is dependency cleaning an effective technique for
reducing the size of dependency metadata?
7.1
Implementation and Setup
We implement Orbe in C++ and use Google’s Protocol Buffers for message serialization. We partition the
data set to a group of servers using consistent hashing
[12]. We run NTP to keep physical clocks synchronized.
NTP can be configured to change the clock frequency to
catch up or fall back to a target. Hence, physical clocks
always move forward during synchronization, a requirement for correctness in Orbe.
As part of the application tier, servers that run Orbe
clients are in the same data center with Orbe partition
servers. A client chooses a partition in its local data
center as its originating partition by a load balancing
scheme. The client then issues all its operations to its
originating partition. If the originating partition does not
store an item required by a client request, it executes the
operation at the local partition that manages the required
item.
Orbe’s underlying key-value store keeps all key-value
pairs in main memory. A key points to a linked list that
contains different versions of the same item. The operation log resides on disk. The system performs group
commit to write multiple updates in one disk write. A
PUT operation inserts a new version to the version chain
of the updated item and adds a record to the operation
log. During replication, replicas of the same partition exchange their operation logs. Each replica replays the log
from other replicas and applies the updates one by one
after dependency checking.
We run the DM-Clock protocol in all experiments,
even where the DM protocol would suffice, because it
is a superset of the DM protocol. We set the heartbeat
broadcasting interval ∆ to 10ms. By default, dependency
cleaning is disabled. We enable it in one experiment,
where we mention its use explicitly (see Section 7.6).
We run experiments on a local cluster where all
servers are connected by a single GigE switch. All
Operation
Throughput
(K op/s)
Echo
GET-10B
PUT-1B
PUT-16B
PUT-128B
71.3
61.4
36.8
36.4
30.2
Table 2: Maximum throughput of client operations on a single
partition server without replication.
servers in the cluster are Dell PowerEdge SC1425 running Linux 3.2.0. Each server has two Intel Xeon processors, 4GB of DDR2 memory, one 7200rpm 160GB
SATA disk, and one GigE network port. The round-trip
network latency in our local cluster is between 120 to
180 microseconds. We enable the hardware cache of
the disk. The latency of writing a small amount of data
(64B) to the disk is around 450 microsecond. We partition the local cluster into multiple logical “data centers”
as necessary. We introduce an additional 120 milliseconds network latency for messages among replicas of
the same partition located at different logical data centers.
7.2
Microbenchmarks
We first evaluate the basic performance characteristics of Orbe through microbenchmarks. We replicate the
data set in two data centers. At each data center, the data
set is partitioned on eight servers. Each partition loads
one million data items during initialization. For each
preloaded item, the size of a key is eight bytes and the
value is ten bytes.
In the first experiment, we examine the capability of a
single partition server. We launch enough clients to saturate the server. A GET operation reads a randomly selected item from its originating partition. The PUT operation also operates on the originating partition by updating a random item with different sizes of update values. For comparison, we also introduce an Echo operation, which simply returns the operation argument to the
clients.
As shown in Table 2, a partition server can process Echo operations at about 70K ops/s, GET operations at about 60K ops/s, and PUT operations at about
30K ops/s. The throughput of Echo indicates the message processing capability of our hardware. As the update value size increases in PUT, the throughput drops
slightly due to the increased cost of memory copies. In
all cases, CPU is the bottleneck.
In the second experiment, we measure operation latencies. For this experiment, GET and PUT choose items
located at the originating partition with a probability of
50% and at other local partitions with the other 50%. A
GET-TX operation reads six items in total. One is from
its originating partition while the other five are from
other local partitions.
Figure 3 shows the latency distribution of the four operations. The Echo operation shows the baseline as it
100
350
Echo
Get
Put
TxGet
60
40
20
0
0
200
400
600
800
Operation latency (microseconds)
Put-Get 1:1
Put-Get 1:8
Put-Get 1:64
TxGet
300
1000
1200
Max Throughput (Kops/sec)
CDF
80
Figure 3: Latency distribution of client operations.
250
200
150
100
50
0
2
7.3
Scalability
We now examine the scalability of Orbe with an increasing number of partitions. We set up two data centers with two to eight partitions at each.
We first use three workloads which are a configurable
mix of PUTs and GETs. Items are selected from the
originating partition with a probability of 50% and from
other local partitions for the other 50%. PUT operations
update items with ten bytes values. For the workload
of read-only transactions, each GET-TX reads one item
from its originating partition and five from other local
partitions. Figure 4 shows the throughput of Orbe as the
number of partitions increases. Regardless of the put:get
ratio, Orbe scales out with an increasing number of partitions. Because Orbe propagates updates across partitions
in parallel, it is able to utilize more servers to provide
higher throughput.
7.4
Comparison with Eventual Consistency
To show the overhead of providing causal consistency in our protocols, we compare Orbe with an eventually consistent key-value store, which is implemented in
Orbe’s codebase. We set up two data centers of three partitions each. A client accesses items randomly selected
from the three local partitions with different put:get ratios. PUT updates an item with a value of 60 bytes.
Figure 5 shows the throughput of Orbe and the eventually consistent key-value store. For an almost read-only
workload, they have similar throughputs. For an almost
update-only workload, Orbe’s throughput is about 24%
lower. The minor degradation in throughput is a reason-
3
4
5
6
Number of Partitions
7
8
Figure 4: Maximum throughput of varied workloads with two
to eight partitions. The legend gives the put:get ratio.
120
110
Max Throughput (Kops/sec)
only takes one round-trip latency to finish. Each GET
and PUT requires either one or two rounds of messages
within the same data center (depending on the location
of the requested item), which results in two clear groups
of latencies. The latency of executing a client operation is low, because Orbe does not require a partition
server to coordinate with its replicas at other data centers to process GET and PUT operations. None of the
(microsecond-scale) client operations depend on replication operations that incur the 120ms latency between
data centers.
100
90
80
70
60
128:1
Orbe
Eventual Consistency
64:1
16:1
4:1
1:1
1:4
Put:Get Ratio
1:16
1:64
1:128
Figure 5: Maximum throughput of workloads with varied
put:get ratios for both Orbe (causal consistency) and eventual
consistency.
able price to pay for the much improved semantics over
eventual consistency.
The major overhead of implementing causal consistency comes from 1) network messages for dependency
checking and 2) processing, storing and transmitting the
dependency metadata. Figure 6 shows this overhead with
two curves. The first is the average number of dependency checking messages per replicated update. The second is the percentage of the dependency metadata in the
update replication traffic in Orbe. When the workload
is almost update-only, the metadata percentage is small
and so is the number of dependency checking messages
per replicated update. When the workload becomes readheavy, the numbers go up, but level off after GETs dominate the workload.
The contents of dependency matrices explain the
numbers in Figure 6. As Orbe tracks only the nearest
dependencies, an update depends only on the previous
update and the reads since the previous update in the
same client session. With a high put:get ratio, the dependency matrix contains only a few non-zero elements.
With a low put:get ratio, reads generate a large number
30%
2
20%
1
10%
0
128:1
64:1
16:1
4:1
1:1
1:4
Put:Get Ratio
1:16
1:64
120
0%
1:128
Figure 6: Average number of dependency checking messages
per replicated update and percentage of dependency metadata
in the update replication traffic with varied put:get ratios in
Orbe.
of dependencies, but the total number of elements in a
dependency matrix is bounded by the number of partition servers in the data store.
100
Max Throughput (Kops/sec)
Orbe dependency check msg
Orbe dependency metadata
Metadata Percentage
Number of Messages
3
80
60
40
Orbe 1:4
COPS 1:4
Orbe 1:0
COPS 1:0
20
0
1
10
100
Average Inter-Operation Delay (milliseconds)
Figure 7: Maximum throughput of operations with varied
inter-operation delays for both Orbe and COPS. The legend
gives the put:get ratio.
Comparison with COPS
We compare Orbe with COPS [17], which also provides causal consistency for both partitioned and replicated data stores. We implement COPS in Orbe’s codebase. For an apples-to-apples comparison, we enable
read-only transaction support in both Orbe and COPS
(which is called COPS-GT in prior work [17]).
COPS explicitly tracks each item version read and updated at the client side. It associates a set of dependency
item versions with each update. A dependency matrix
in Orbe plays the same role as a set of dependency item
versions in COPS, but most of the time it takes less space
using sparse encoding.
Although COPS relies on a number of techniques to
reduce the size of dependency metadata, it can still become considerable since COPS has to track the complete
dependencies to support read-only transactions while
Orbe only tracks the nearest dependencies. In addition,
the execution time of the two-round transactional reading protocol in COPS limits the frequency of garbagecollecting the dependency metadata. During the fixed interval between two successive garbage collections, the
more operations a client issues, the more dependency
states it creates. Hence, the size of dependency metadata is highly related to the inter-operation delays at each
client. COPS sets the garbage collection interval to six
seconds [17]. We use the same value in our COPS implementation.
We set up two data centers of three partitions each.
A client accesses data items randomly selected from the
three partitions with a configurable put:get ratio. Figure
7 illustrates the throughput of Orbe and COPS with different client inter-operation delays. Figure 8 shows the
average number of states on which an update depends.
For COPS, this is the number of dependency item versions. For Orbe, this is the number of non-zero elements
in the dependency matrix. Orbe provides consistently
Number of Dependencies
1400
7.5
1000
Orbe 1:4
COPS 1:4
Orbe 1:0
COPS 1:0
1200
1000
800
600
400
200
0
1
10
100
Average Inter-Operation Delay (milliseconds)
1000
Figure 8: Average number of dependencies for each PUT operation with varied inter-operation delays for both Orbe and
COPS. The legend gives the put:get ratio.
higher throughput than COPS as it tracks fewer dependency states and spends fewer CPU cycles on message
serialization and transmission. Figure 8 suggests that
Orbe and COPS should have similar throughput when
the inter-operation delays are longer than one second.
By tracking fewer dependency states and efficiently
encoding the dependency matrix, Orbe also reduces the
inter-datacenter network traffic for update replication
among replicas of the same partition. Figure 9 compares
the aggregated replication traffic (transmission only) between Orbe and COPS.
Tracking fewer states at the client side reduces the
client’s memory footprint, but also consumes fewer CPU
cycles as fewer temporary objects are created and destroyed for tracking dependencies. Figure 10 shows the
CPU utilization of a server that runs a group of clients
for Orbe and COPS, separately. For this measurement,
we run all clients at a single powerful server to saturate the data store and record the CPU utilization of the
server. Orbe is more efficient. It uses fewer CPU cycles
per operation as it manages fewer states.
7.6
Dependency Cleaning
Dependency cleaning removes the necessity for dependency tracking when a client reads a fully replicated
Orbe 1:4
COPS 1:4
Orbe 1:0
COPS 1:0
180
160
Max Throughput (Kops/sec)
Aggregated Replication Traffic (Mbps)
200
140
120
100
80
110
105
100
95
90
85
80
Dependency Cleaning Disabled
Dependency Cleaning Enabled
75
70
1
60
2
3
40
20
0
1
10
100
Average Inter-Operation Delay (milliseconds)
1000
4
5
Number of Partitions
6
7
8
Figure 11: Maximum throughput of operations with and without dependency cleaning enabled.
Replication Traffic (Mbps)
12
Figure 9: Aggregated replication transmission traffic across
data centers with varied inter-operation delays for both Orbe
and COPS. The legend gives the put:get ratio.
120%
Orbe 1:4
COPS 1:4
Orbe 1:0
COPS 1:0
CPU Utilization
100%
10
8
6
4
2
Dependency Cleaning Disabled
Dependency Cleaning Enabled
0
1
2
3
4
5
Number of Partitions
6
7
8
80%
Figure 12: Aggregated replication transmission traffic with
and without dependency cleaning enabled.
60%
40%
20%
0%
1
10
100
Average Inter-Operation Delay (milliseconds)
1000
Figure 10: CPU utilization of a server that runs a group of
clients with varied inter-operation delays for both Orbe and
COPS. The legend gives the put:get ratio.
item version. However, it increases the cost of update
replication as it requires additional inter-datacenter messages to mark an item version as fully replicated.
In this experiment, we show the benefits of dependency cleaning for workloads that read from a large
number of partitions and update only a few. We set up
two data centers and vary the number of partitions from
one to eight at each data center. A client reads a randomly selected item from each of the local partitions and
updates one random item at its originating partition.
Figure 11 shows the maximum throughput of Orbe
with and without dependency cleaning enabled. When
the system has only one partition, all reads and updates go to that partition. Dependency cleaning does
not help as no network message is required for dependency checking. In this case, the throughput of Orbe
with dependency cleaning enabled is slightly lower, because it requires more messages for update replication. However, the throughput drop is small, because
we let update replication messages piggyback replication acknowledgement and full-replication completion
messages and batch these messages whenever possible.
As we increase the number of partitions, the throughput of Orbe with dependency cleaning enabled is higher.
The throughput gap increases as the system has more
partitions. With dependency cleaning, an update does
not depend on states from other partitions most of the
time, although it reads states from those partitions. As a
result, dependency checking on replicated updates does
not incur network messages at the remote data center. By
removing this part of the overhead, dependency cleaning
helps the overall throughput.
Dependency cleaning also reduces the size of dependency metadata for an update. Figure 12 shows the aggregated replication traffic from all partitions. The traffic
decreases as the number of partitions increases because
the put:get ratio decreases. Figure 13 shows the average
percentage of metadata in the update replication traffic.
8
Related Work
There have been many causally consistent systems in the
literature, such as lazy replication [13], Bayou [22], and
WinFS [19]. They use various techniques derived from
the causal memory algorithm [2]. However, these systems target only full replication. None of them considers
scalable causal consistency for partitioned and replicated
data stores, to which Orbe provides a solution.
COPS [17] identifies the problem of causal consistency for both partitioned and replicated data stores and
gives a solution. It tracks every accessed state as dependency metadata at the client side. To support causally
Metadata Percentage
60%
50%
40%
30%
20%
10%
Dependency Cleaning Disabled
Dependency Cleaning Enabled
0%
1
2
3
4
5
Number of Partitions
6
7
8
Figure 13: Average percentage of dependency metadata in update replication traffic with and without dependency cleaning
enabled.
consistent read-only transactions, a client has to track
the complete dependencies explicitly. Although COPS
garbage-collects the dependency metadata periodically,
the metadata size may still be large under many workloads and can affect performance. In comparison, Orbe
relies on dependency matrices to track the nearest dependencies and keeps the dependency metadata small and
bounded. Orbe provides causally consistent read-only
transactions using loosely synchronized clocks. Orbe requires one round of messages to execute a read-only
transaction in the failure-free mode while COPS requires
maximum two rounds.
Eiger [18] is recent follow-up work on COPS and provides causal consistency for a distributed column store.
It proposes a new protocol for read-only transactions
using Lamport clock [14]. Although Eiger also needs
maximum two rounds of messages to execute a readonly transaction, a client tracks only the nearest dependencies. In addition, Eiger provides causally consistent update-only transactions. Eiger still tracks every accessed state at the client side.
ChainReaction [3] implements causal consistency on
top of chain replication [23]. ChainReaction also tracks
every accessed state at the client side. To solve the problem of large dependency metadata when providing readonly transactions, it uses a global sequencer service at
each data center to totally order update operations and
read-only transactions. However, the sequencer service
increases the latency of all update operations by one
round-trip network latency within the data center and is
a potential performance bottleneck. In comparison, Orbe
does not have any centralized component. It provides
causal consistency for update-anywhere replication and
relies on loosely synchronized physical clocks to implement read-only transactions.
Bolt-on causal consistency [5] provides causal consistency to existing eventually consistent data stores. It
inserts a shim-layer between the data store and the application layer to insure the safety properties of causal consistency. It relies on the application to maintain explicit
causality relationships. Tracking causality based on application semantics is precise but requires the applica-
tion developers to specify causal relationships among
application operations. In contrast, Orbe provides causal
consistency directly in the data store, without requiring
coordination from the application.
Physical clocks have been used in many distributed
systems. For example, Spanner [8] implements serializable transactions in a geographically replicated and
partitioned data store. It provides external consistency
[11] based on synchronized clocks with bounded uncertainty, called TrueTime, requiring access to GPS and
atomic clocks. Clock-SI [9] uses loosely synchronized
clocks to provide snapshot isolation [6] to transactions
in a purely partitioned data store. In comparison, Orbe
targets causal consistency, a weaker consistency model.
It provides causally consistent read-only transactions using loosely synchronized clocks in a partitioned and
replicated data store.
9
Conclusion
In this paper, we propose two scalable protocols that efficiently provide causal consistency for partitioned and
replicated data stores. The DM protocol extends version vectors to two-dimensional dependency matrices
and relies on the transitivity of causality to keep dependency metadata small and bounded. The DM-Clock protocol relies on loosely synchronized physical clocks to
provide causally consistent read-only transactions. We
implement the two protocols in a distributed key-value
store. We show that they incur relatively small overhead
for tracking causal dependencies and outperform a prior
approach based on explicit dependency tracking.
Acknowledgments. We thank the SOCC program committee and especially our shepherd, Indranil Gupta, for
their constructive feedback. Daniele Sciascia also provided useful comments on final revisions of this work.
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